Reproduction of a desired multi zone sound field over a region of interest has drawn the attention of researchers in recent years. However, the majority of existing works in this area do not take into account the reverberant environments that practical multi zone sound reproduction systems will encounter. The reverberation compensation process is difficult to handle due to the unknown reverberant room channel and the large number of loudspeakers and microphones required by existing sound field reproduction systems.
Reverberation is the collection of reflected sounds from the surfaces in an enclosure. It is created when a sound or signal is reflected in an enclosed environment that leads to a large number of reflections and then gradually decay as the sound is absorbed by walls, scatterers and air. This is most noticeable when the sound source stops but the reflections continue to exist till they reach zero amplitude. The majority of the sound field reproduction techniques are designed with free-field assumption, but this is not the case in most real implementations.
Room reverberation poses a major challenge in sound field reproduction and the unwanted reverberation generally leads to poor sound field reproduction and localization confusion for the listeners. Therefore, reverberation cancelation techniques are indispensable for a reproduction system with real-world settings. The most natural approaches are the passive techniques. For example, the room can be equipped with acoustic absorption materials, so that a modest attenuation of sound reflection is provided. However, the related costs pose a major challenge for this method and it is difficult to realize in many real-world application scenarios (e.g., sound field reproduction in an office or home environment). More technically advanced passive approaches may use fixed or variable directivity higher order loudspeakers in order to minimize the sound radiation directing towards the walls of a room. However, it requires some specific sound reproduction apparatus, which is difficult to achieve in practice.
To equalize the room reverberation, the inverse of the room response is generally applied to loudspeaker driving signals. Techniques have been suggested that are based on mode matching to reproduce a single-zone sound field accurately over the entire control region in reverberant rooms. An approach of reproducing a multi zone sound field within a desired region using sparse methods was introduced. This allowed a reduced number of randomly placed measurements to sparsely estimate the room transfer functions from the loudspeakers over the desired region in the domain of plane wave decomposition. The estimates were then used to derive the optimal least-squares solution for the loudspeaker filter gains. For these approaches, a prior measurement of the room transfer function for all the employed loudspeakers was needed. This is time-consuming to implement in practice and its performance is vulnerable to any changes in the ambient environment conditions during the measurement process.
Wave Domain Adaptive Filtering (WDAF) is a more practical approach to the application of reverberation cancelation in sound field reproduction. It has been introduced to active listening room compensation in Wave Field Synthesis systems. The wave-domain representation of the sound field was described using transformations on the microphone array input and the loudspeaker output respectively. These techniques suffer from practical issues, e.g. a large number of microphones are required for the room channel estimation. Additionally, the adaptive processes in these techniques are shown to diverge in some reverberant environments that feature low direct-to-reverberant-path power ratios. The iterative calculation of the pseudoinverse in each iteration is needed, which may lead to ill-conditioning problems and channel estimation errors.